Conventionally, a patent document 1 discloses a technique to cause an engine rotational speed to fall as low as possible during traveling, and then perform downshifting at lower speed, in order to improve fuel efficiency.
However, when downshifting is performed at low vehicle speed, the downshifting occurs under a drive condition, because the engine rotational speed cannot fall is below an idling rotational speed. In this situation, there is a problem that a pushing shock is likely to occur also because of a torque amplification effect of a torque converter. Especially, when a pushing shock is caused by downshifting during coasting, the pushing shock causes a driver to feel uncomfortable, because the pushing shock is not a result from a driver's request for driving force.